Resistance can be depicted as the ratio between the applied voltage to the current flowing through a circuit. The S.I. unit of resistance is Ohms (Ω).
Determine the Given Data
Initial resistance on the wire, Ri = 4 Ω
Assuming that the initial length of the wire = Li.
As per the given equation, the final length of the wire Lf =2Li
Consider area of the wire = A.
Consider the resistivity of the wire = ρ.
Consider final resistance of the wire = Rf.
Formula Used
We know that resistance is given as,
⇒ \(R = \rho{{L} \over A}\)
⇒ \(\rho= {{RA} \over L}\)
Calculation of New Resistance
Since the resistivity of the wire remains the same in both, we can mention:
\(\rho = {{R_i A} \over L_i} = {{R_fA} \over L_f}\)
⇒ \({{R_i} \over L_i} = {{R_f} \over L_f}\)
Upon value substitution, we can get,
\({{4} \over Li} = {{R_f} \over 2L_i}\)
⇒ Rf = 8 \(\Omega\)
Therefore, the new resistance is 8\(\Omega\).
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